How to wrap fingers around a cylinder (handle)?
You can rotate portions of the mesh around the 3D cursor. The position can be established by first selecting a ring of vertices in Edit Mode, and then ShiftS and choosing cursor to selected. Press the period key . to choose the 3D cursor location as the rotation point. Select the rest of the mesh you wish to rotate and ...rotate.



Perhaps later you will want to rig to accomplish the same thing - in which case you will want to create your mesh from quads to avoid distortion. In this case I used ALTJ to convert the tris to quads and re-distributed the vertices. The rotation also has proportional editing enabled. While bones and weight paint can achieve the same thing, this is a good way to test bends.